Context. Many aspects of massive star ( > ∼ 10 M ) formation are still unclear. In particular, the outflow properties at close distance (100-1000 AU) from a massive young stellar object (MYSO) are not yet well established. Aims. This work presents a detailed study of the gas kinematics toward the hot molecular core (HMC) G31.41+0.31. Methods. To study the HMC 3D kinematics at milli-arcsecond angular resolution, we performed multi-epoch VLBI observations of the H 2 O 22 GHz and CH 3 OH 6.7 GHz masers, and single-epoch VLBI of the OH 1.6 GHz masers. Results. Water masers present a symmetric spatial distribution with respect to the HMC center, where two nearby (0. 2 apart), compact, VLA sources (labeled "A" and "B") are previously detected. The spatial distribution of a first group of water masers, named "J1", is well fit with an elliptical profile, and the maser proper motions mainly diverge from the ellipse center, with average speed of 36 km s −1 . These findings strongly suggest that the "J1" water maser group traces the heads of a young (dynamical time of 1.3 × 10 3 yr), powerful (momentum rate of 0.2 M yr −1 km s −1 ), collimated (semi-opening angle 10 • ) jet emerging from a MYSO located close (within ≈0. 15) to the VLA source "B". Most of the water features not belonging to "J1" present an elongated (≈2 in size), NE-SW oriented (PA ≈ 70 • ), S-shape distribution, which we denote with the label "J2". The elongated distribution of the "J2" group and the direction of motion, approximately parallel to the direction of elongation, of most "J2" water masers suggests the presence of another collimated outflow, emitted from a MYSO placed near the VLA source "A". The proper motions of the CH 3 OH 6.7 GHz masers, mostly diverging from the HMC center, also witness the expansion of the HMC gas driven by the "J1" and "J2" jets. The orientation (PA ≈ 70 • ) of the "J2" jet agrees well with that (PA = 68 • ) of the well-defined V LSR gradient across the HMC revealed by previous interferometric, thermal line observations. Furthermore, the "J2" jet is powerful enough to sustain the large momentum rate, 0.3 M yr −1 km s −1 , estimated from the interferometric, molecular line data in the assumption that the V LSR gradient represents a collimated outflow. These two facts lead us to favor the interpretation of the V LSR gradient across the G31.41+0.31 HMC in terms of a compact and collimated outflow.